where \(\Theta \)  denotes a hypocontinuous, bilinear map from \({\mathcal {O}}_M({\mathcal {L}}(X,Y))\times {\mathcal {S}}^{\prime }(X)\)  into \({\mathcal {S}}^{\prime }(Y)\)  (see [1]}).
The multipliers symbols, which are involved in the study of maximal regularity property of evolution equations usually are of \({\mathcal {O}}_M\) -class; see, e.g. Proposition REF . For instance, it is the case of the problem (REF ) discussed in Section , where the solution operator \(U\)  is given by a multiplier \(a(D)\)  with \(a = (i\cdot + A)^{-1} \in {\mathcal {O}}_M({\mathcal {L}}(X,Y))\)  and \(Y:=D_A\) .
